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it was shown, how this one-dimensional transformation principle can be 
extended to two-dimensional transformations. Thereby, using two seccessively 
performable transformations in row and column direction, in connection with 
a decoupling of the transforming function, exactly the above mentioned 
algorithmic dimension reduction is realized. 
Orthogonality is the decisive mathematical aid for decoupling the co-ordinate 
axes. With those orthogonalitiy relations two-dimensional procsses can be 
divided into two independent one-dimensional processes. A classic example for 
that are the integral transformations, because the corresponding characteristic 
functions fulfill exactly this orthogonality. The example of the two-dimensional 
FOURIER transformation is sufficiently known, which can be realized as twofold 
one-dimensional FOURIER transformation in each co-ordinate. 
4. Prospects 
Each problem to be solved has got corresponding data structures, which have a 
natural dimension. Many problems in photogrammetry and neighbouring disciplines 
in geoinformatics have got a two-dimensional position reference, completed by a 
semantic feature. With the help of the stereoscopic principle the terrain 
altitude can be determined as special "feature", which can also be related to 
a two-dimensionally structured situation. 
Besides the dimensionality of data the basic structuring - raster or vector 
data - is of decisive importance. Vector-oriented data, which are produced 
within the photogrammetric plotting process especially during the derivation 
of cartography-oriented data bases, are naturally unproblematic in regard of 
the dimension number. Raster-oriented data - e. g. digital image structures - 
with a sequential order basically contradict former photogrammetric approaches. 
The term (p, x) means, that the feature p exists in the place x. 
The transformation T thereby means, that this is also decomposed in regard of 
feature and space: 
T - T(M,G). 
There is M = M(p) und G = G(x).